Method of producing curved tooth gearing



Dec. 4, 1928.

E. WHLDH ABER METHOD OF PRQDUCIN'G GURVED TOOTH GEARING Filed Nov. 8,1924 4 Sheets-Sheet 1 V IIYVENTORJY A Ermasi was? in A v" 1! 121:5ATTORNEY E. WILDHABER METHOD OF PRODUCING CURVED TOOTH GEARING Dec. 4,1928.

4 Sheets-Sheet Filed Nov. 8, 1924 Dec. 4, 1928. 1,693fi86 E. WILDHABERMETHOD OF PRODUCING CURVED TOOTH GEARING Filed Nov. 1924 4 Sheets-Sheet4 I I VENTOR. Erzesi er 1 Z'SATTORNEY Patented Dec. 41, 1928,

our it PATENT drama,

ERNEST WILDHABER, OF ROCHESTER, NEW YORK, ASSIGNOR T GLEASON WORKS, OF

- ROCHESTER, NEW YORK, A CORPORATION OF NEW YORK.

METHOD OF PRODUCING CU RVED TOOTH GEARING.

Application filed November 8, 1924. Serial N'o. 743,572.

This invention relates to gearing and more particularly, to the varietyhaving longitudinally curved teeth, one object of the invention being toprovide a new and efficient system of gearing of this character togetherwith an improved method for producing the same of a more simple andrapid character than here- I tofore employed, as well as new andimproved tool means for carrying out the novel method.

Another object is the provision of a system of curved tooth gearingproduced by a meshing action between cutter and blank based upon thetheory of meshing of hyperboloid gears.

Another object is to provide a more simple and expeditious method forproducing curved tooth tapered gears. More specifically, it-is a purposeof the invention to provide an advantageousmethod for producing suchgears in which one of a mating pair is'cut by a continuous indexingrotation of tool and blank combined with a simple relative feedingmovement there'between without the usual generating roll, with theresultant advantages of increased simplicity and speed of production. v

' Another object is to provide a method of producing tapered gearscomprising the use of the advantageousprinciple of simultaneous rotationof tool and blank in continuous cutting and indexing relation, incombination with the use of a gear so cut as the basis of the system ofgearing of which it forms a part.

A further object is to provide practical and economical tool means forcarrying out the above method and specifically a hobbing cuttured andmaintained in condition in use. To these and other ends the inventionresides in certain improvements and combinations of parts. all as willbe hereinafter more fully described, thenovel features being pointed outin the claims at the end of the specification.

y In the drawings:

Figure 1 is a diagrammatic plan View of a tapered hob and beveled gearblank arranged in cutting contact in accordance with a method embodyingthe present invention;

ter of a form adapted to be easily manufac Figure 2 is an elevation ofthe same; Figure 3 is a schematic plan view of a pair of tapered hobsarranged in intermeshing relation to further illustrate the method;

Figure 4 is an elevation of the same; Figure 5 is a schematic plan viewof a ta- Dered hob and pinion blankarranged for cutting the latter inaccordance with the inven tion;

Figure 6 is an elevation of the same; Figure 7 is a schematic plan viewof a pair of hyperboloid gears arranged in int'ermeshing relation;Figure 8 is. an elevation of the same; Figure 9 is a schematic elevationof a pair of intermeshing hyperboloid gears of hob form;

Figure 10 is a side view of a tapered hob embodying the invention, shownpartly in section;

Figure 11 is a fragmentary end View of the same showing the flutes;

Figure 12 is a side View of the same with the cutting blades in sectionto further illustrate their character and arrangement;

Figure 13 is a diagrammatic view illustrative of certain structuraldetails of the ho v Figure 14 is an elevation of a curved tooth beveledgear produced in accordance with and embodying-the present invention,and showing schematically a'hobbing cutter arranged in cutting contacttherewith;

Figure 15 is a sectional plan view of the gear on the line 15 -15 inFigure 14, and

Figure 16 is a sectional plan view of a portion of the gear on the line16"16 in Figure 14. 7

Similar reference numerals throughout the tooth gears, and of ananalysis to that end of the theory of action of hyperboloid gearing; Thelatter involves the meshing of a pair of gears with the axis of oneoffset from that of the other, and the present method involves thecuttingof curved tooth bevel gears by an analogous arrangement in whichthe axis of the tool is offset from that of the gear blank.

While the invention may be carried out by the use of various tool means,it has been discovered that one advantageous embodiment comprises theuse of a. tapered hob andthat such a hob can be made to mesh along astraight line with a gear of suitable construction which forms the basisof the system of gearing produced and can be cut and finished y the hobin complete form without resort to the usual generating roll. Thepresent embodiment of the invention in conjunction with the use of sucha hob is illustrated diagrammatically in Figures 1 to 6 and will firstbe described in a more general way, followed by a particular descriptionof the principles involved as well as of the hobbing cutter and thegears produced thereby in accordance with the method.

Figure 1 shows in plan view a tapered hob 20 arranged in cutting contactwith a bevel gear blank 21, with the axis 22 of the hob offset from theaxis 23 of the gear, as more particularly described hereafter. The hoband blank are rotated about their respective axes in timed, intermeshingrelation to effect a continuous cutting and indexing action between theteeth of the hob and those to be cut in the blank, and a relativefeeding movement is simultaneously produced between the hob and blankparallel with the axis 23 of the latter to obtain the desired toothheight, so that in effect, the hob is sunk into the blank to the fulldepth of the teeth being out. It is to be noted that the manipulation ofthe hob and blank comprises exclusively the cutting and indexingrotation and the simple feeding movement described which may be rapidlyaccomplished without the necessity of resort to the time consumingrelative rolling movement between the parts commonly required togenerate the tooth The hob is formed by longitudinally gashing andrelieving a tapered worm to produce cutting portions of rack section andconstant pitch in a. plane offset from the axis of the hob, as morefully described hereafter. The gear produced is a curved tooth bevelgear of rack section and uniform pitch along a straight line in a planeoifset from its axis and inclined with respect to the projection of itsaxis in said plane, as more fully appears hereinafter.

It has also been found that another hob can be made to mesh with hob 20in the same way that the latter meshes with the basic ear 21. That is tosay, a second or counter ob 24, F1gures 3 and 4, can be made to meshinternally with and sweep out the teeth of the basic gear 21 so as torepresent the latter when swung about its axis 23. i A counter hob ofthis nature may therefore be employed, Figures 5 and 6, to cut a gear orpinion capable of meshing correctly with the basic gear 21. In cuttingthe mating gear reeaese 25 the counter hob and blank are rotated abouttheir respective axes 26 and 27 to produce a continuous intermeshingindexing of the hob and blank teeth while a relative generating roll isproduced between the hob and blank about the axis 23 of the imaginarygear 21 upon which the mating gear 25 may be assumed to roll. The anglebetween the axis 27 of the mating gear and axis 23 is a right angle, asshown in Figure 6, and the generatin roll about axis 23 is added to orsubtracte from the indexing rotation of the hob or blank 25 rolled aboutthis axis. It will thus be seen that the gear 21, which serves as thebasis of the system is cut in a simple and rapid manner by merelysinking the hob into it withoutthe generating roll, while the matinggear or pinion 25 is out wit-h a similar hob in a rapidand practicalmanner, involving a relative generating roll of which the mating gear isthe basis.

The principles involved in the above described method of producing thegearing are best explained by a consideration of the theory of meshingof liyperboloid gears which latter may be described generally as gearshaving tapered bo'dy portions rotating on non-intersection axes. Suchgears approach the nature of beveled gears where the distance betweenthe axes of the mating pair is comparatively small and they approach theform of worm gears as such distance becomes large. Thus in Figures 7 and8, 28 and 29 represent a pair of such gears in intermeshing relation.Gear 28 rotates upon an axis A while gear 29 rotates on an .axis A whichaxes are parallel to the plane of the paper in Figure 7, but are oifsetfrom one another at a distance E as shown in Figure 8. Let N representthe number of teeth in gear 28 and N the number of teeth in gear 29, sothat the tooth ratio is N/N The tooth shapes and characteristics of meshdepend solely upon the above ratio, but for convenience in the followingexplanation, a velocity analysis will also be made.

If a point P, Figures7 and 8, be assumed to travelin space along anyassumed line, it will trace a relative path with respect to gear 28 andanother relative patli with respect to gear 29, which paths join at P.Such a point P can be a point of-mesh between the two gears when thetangents to the two relative paths coincide, that is when these pathshave axes A and A andthat convenient symbols be employed asfollows: Q Yw a bsolute velocity of P in a plane parallel to axes A' and A a, aanglesbetween, the .direction of I Wand the axes A and A respectively. aV =relative velocity component of P with respect t o gear 28 iiithe'direction of W. V relative velocity component of I P with respect togear28 perpendicular; to W in apIane,

parallelto axes A and A V,'=relative -lvelocity component of P,with-respect to gear 28 in the direction Z, or perpendicularto a planeparallel to axes ,A, A

V ,V., V =corresponding components of relative'velocity of P .Withrespect to gear 29.

Q, Q,,=angular velocities of gears 28 and 29, respectively.

Z, Z constant vertical distances of the above values may besubstitutedtlierein J to give after reduction, the following equation:'

d Z1 cos a, I (Z Z cos a The last equation is a constant, a- 'and abeing assumed constant. For other points in the \same plane, as P,Figures 7 and 8, the ratio is always the same, hence all such points liein a straight line G passing I-lobs are commonly single threaded,thatis,

=1. Gear 28 itself may be considered as memes Hence line G through thepoint 0, and only points lying in such straight lines are capable ofproduc- .ingrelative pitch h perboloids contact with one another along t1e straight line of action G and the threads or teeth of correspondinggears can meshvalong this line. The location of the line can be found byletting S represent the distance of point P from 0, so that I h 1 tan at tan (a, Z Line G is the generatrix of the pitch surfaces of the gears,which are hyperboloids since the line is offset from the axis of each.

Taking up the second condition represented by the equation d Ssino.Zcosa LLB HO H and the relations ai 112 1 Z 21r ,an 9 21 paths with acommon tangent. is the line of action and the-two where L==lead pertooth and N N=the number of teeth, by substituting the above values andreducing expressions for the values of Z and Z can be readily obtainedas follows tana (,N N tan a+ tan a, 211- sin (t sin a tan-a X L N 0 N Ftan a+tan a 27! sin a, sin a,

By adding these equations the following expression is obtained for thecenter distance E; (Z+Z Figure 8:

L N 'N sin a] sin (t It is to be noted that all of the other factors ofthe above equation being constants,

the lead L also is constant, and the gears will have a constant pitchalong line G.

t Gear 29 can also be considered as a hob. This hob will therefore havea constant pitch along line G and is preferably of rack section alongthe latter, and will therefore produce a gear whose teeth'are andracksection along the line of action. It

of constant pitch can mesh in the same way with different Y gears 28 solong as their angles,"a and tooth numbers N fulfill the equation givenabove for Z;,. The number N can be expressed as a function of a asfollows sin a L i t single threaded'or as a hoband will for conveniencebe referred to in this aspect as the counter hob will therefore have thesamepitch and rack section as the gear 28 itself and it is thereforecapable of representing hob 2 l-and pinion 25 is in the equivalent thegear, in cutting a-mating gear, when given suitable generating orfeeding motionabout the axis of said gear. The counter hob must ofcourse fulfill the above equation for N. It is therefore possible to hoba gear, preferably the larger gear of a pair without additionalgenerating roll and to cut the mating gear with the counter hob with arelative generating movement about the apex of the blank as. if theblank were rolling on its mating gear, as described above in connectionwith Figures 1 to 6 inclusive.

As already stated, the rotation of the line of action G about the axisof the gear generates a hyperboloidal surface. This is shown at 30, Fig.10, in connection with a hob 31 embodying the invention, and at 32, Fig.15, in connection with a gear 33 produced thereby. The angle a and theoffset Z are so chosen that the said hyperboloidal surface approximateseither, the pitch cone of the gear or the conical surfaces which liesmidway between the root and face cones of the gear. The profile 32 ofsuch hyperboloidal surface is shown in dotted line as tangent to theprofile 34, Fig. 15, of the latter of such conical surfaces.

The tapers of hob and counter hob can be made alike when the hob isgiven characteristics corresponding to the above equation for the valueof Z which reduces, N being equal L to unity, to the form sm a In thiscase the formula for N given above reduces to cos a sin a N= 2 sin a cosa In practice the hob and counter hob are preferably alike inconstruction and in fact one and the same hob is employed as both hoband counter hob. This hob will out the gear without generating roll andthe mating pinion with a generating roll corresponding to the meshbetween the gear and pinion, or, in other words, as if the pinion wererolling on the gear in accordance with the principles already describedin' connection with Figs. 5 and 6. where however the relative rollbetween form of actual rolling of the hob.

The construction of the hob is shown in Figures 10 to 13 inclusive ashaving generally the form of a tapered worm gashed longitudinally orfluted as at 35 and relieved as shown to produce cutting blades 36 ofrack section and constant pitch in a plane 139-13, Fig. 11, offset fromthe axis A of the hob a distance Z as heretofore described. The cuttingfaces 37 of the teeth are preferably though not necessarily located insaid plane.

The hob meshes along this offset straight line of action and ispreferably provided with rake or hook flutes, that is, with non-radialflutes 35, as shown in Figure 11, which contain the line of action andare parallel to the hob axis. The relieving tool 38 is led at uniformleadalong the line of action and is preferably positioned above centercorresponding to the desired offset of the hob. With the use of suchrake flutes, improved cutting qualities are combined in this type oftapered hob with mathematical correctness. Figure 13 showsdiagrammatically one of the straight flutes having cutting portions ofuniform pitch or lead and preferably rack section. The hob can cut gearsof various tooth numbers N and taper angles a bearing the relationsexpressed in the simplified equation for N already given. The taperangle a (not the cone angle) may be accurately determined by solving fora in the last equation for N above. The angle a is required for hobsettings. In cutting the gear the hob distance is Z +YZ which can beobtained from the above equations. The inclination of the hob axis is a.(90a). In cutting the pinion, the hob distance is ZZ., and theinclination of the hob axis is a (9O a). A hob can cut practically allgears corresponding to pinions of a given tooth number irrespective oftheir cone angles and a wide range of gears can therefore be cut withcomparatively few hobs.

The gear produced by the above method and hob means is illustrated inFigures 14, 15and 16 which show the line of action G in a plane offsetfrom the axis ofthe gear and inclined with respect to the projection ofsaid axis in said plane. The teeth are of rack section and uniform pitchin such line and it follows from the method described that the teeth ofthe gear are of substantially straight profile and noncircularlengthwise curvature and therefore of constantly changingradius. Asection through the gear in a plane passing through a plurality of itsteeth, as shown for example in Fig. 16, is of the same general form as acorresponding section through-the hob employed to produce it. -When thesame hob is used for cutting gearand pinion as is preferable, the dataof the gear fulfill the following equation v movement without generatingroll by which the gear is cut as described above and the arrangement ofthe hob during such cutting. in contact with the whole tooth surface,makes it practical to employ a. high rate of feed which is preferablyreduced as the teeth near completion for the purpose of completing thework with the desired finish. The described method is not only capableof being carried out by application to known forms of gear its axis andinclined to the projection of its axis in said plane, and in rotatingsaid outter in engagement with the blank.

2. The method of cutting a gear blank consisting in employing a cutterhaving a uniform pitch along a line in a plane ofiset from its axis andinclined to the projection of its axis in said plane, in rotating saidcutter in engagement with the blank, and in simultaneously efi'ecting arelative feeding movement therebetween to obtain the desired height oftooth.

3. The method of cutting a gear blank consisting in employing a hobhaving a uniform pitch along a line in a plane offset from its axis andinclined to the projection of its axis in said plane, and in rotatingsaid hob and blank in continuous cutting engagement with each other.

4:. The method of cutting a gear blank consisting in employing a hobhaving a uniform pitch along a line in a plane olfset from its axis andinclined to the projection of its axis in said plane, in rotating saidhob and blank in continuous cutting engagement with each other and insimultaneously effecting a relative feeding movement therebetween toobtain the desired tooth height.

5. The method of cutting a gear blank consisting in employing a hobhaving .a uniform pitch along a line in a plane ofiset from its axis andinclined to the projection of its axis in said plane, in rotating saidhob and blank in continuous cutting engagement with eachother, and insimultaneously eifecting a relative feeding movement therebetween toobtain the desired tooth height While maintaining a fixed angularrelation between the hob and blank axes so that in finish cuttingposition the hob sweeps the entire width of the toothsurface.

6. The method of cutting a gear which comprises rotating a taper hob ofconstant pitch in a plane offset from its rotary axis in cuttingengagement with a rotating blank.

7. The method of cutting a gear consisting in rotating a taper hob ofconstant pitch in a sectional plane offset from its rotary axis incutting engagement with a rotating blank while maintaininga fixedangular relation between the hob and blank axes 8. The inethod ofcutting a gear consisting in rotating a taper hob of constant pitch in asectional plane offset from its rotary axis in cutting engagement with arotating blank and simultaneously effecting a relative feeding movementbetween the hob and blank to obtain the desired tooth height whilemaintaining a fixed angular relation between their axes.

9. A method of cutting a pair of gears comprisin cutting teeth in onegear with a taper hobiiy rotating said hob in continuous meshingengagement with a continuously rotating tapered gear blank and cuttingthe teeth of the other gear with a hob of the same hand as the first hobby rotating said latter hob in continuous engagement with a rotatinggear blank while imparting a relative rolling movement between thelatter hob and the blank.

10. The method of cutting a tapered gear which consists in rotating ahob in continuous cutting engagement with a rotating blank whileimparting an additional relative movement between hob and blank as ifsaid blank were rolling with its mategear.

11. The method of cutting a pair of gears which comprises cutting onemember of the pair by rotating a hob in cutting engagement with arotating blank and cutting the other member by rotating a hob of thesame hand in cutting engagement with a rotating blank while imparting anadditional relative movement between tool and blank as of a cone rollingon the first gear.

12. A method of cutting a pair of gears which comprises rotating a taperhob in engagement with a rotating blank and cutting the other gear by ataper hob of the same hand rotated in engagement with a rotating blankwhile impartingan additional relative movement between the hob and blankas of a gear rolling on the first gear.

18. A method of cutting a pair of gears which comprises cutting onemember of the pair by rotating a taper hob in engagement with a rotatingblank and cutting the other member of the pair by rotating a taper hobadapted to mesh with the first hob in engagement with a rotating blankwhile imparting an additional relative movement between said second hobarrd blank in the manner of a gear rolling on the first gear.

14. The method of cutting a pairof bevel gears which comprises cuttingone member of the pair by rotating a hob in continuous engagement with arotating blank while maintaining the axis of the hob in offset relationto the axis of the blank and cutting the other member byrotating the hobwhich is adapted to mesh with the complement of the first gear incontinuous cutting engagement with a rotating blank while maintainingthe axis of the hob in offset relation to the axis of the blank andimparting an additional relative movement between hob and blank as of agear rolling on the first gear.

15. The method of cutting a, pair of bevel gears which comprises cuttingone member of the pair by rotating a taper hob in continuous engagementwith a rotating blank while maintaining the axis of the hob in 0&- setrelation to the axis of the blank and cutting the other member byrotating a hob of the same hand as the first hob in continuous cuttingengagement with a rotating blank while maintaining the axis of the hobin 0&- set relation to the axis of the blank and imparting an additionalrelative movement between tool and blank as of a gear rolling on thefirst gear.

16.'The method of cutting a beveled gear having a uniform pitch along astraight line in a plane offset from its axis and inclined to Tan a ZTan a 17 The method of cutting a pair of gears having longitudinallycurved teeth comprising cutting one of the pair by rotating a taper hoband a gear blank in continuous intermeshing engagement while imparting arelative feedmovement between said hob and blank so that in finishcuttin position the hob sweeps out the whole finis ed tooth surface ofthe blank, and in cutting. the other member of the pair by rotating ataper hob and a gear blank in continuous intermeshing engagement whileimparting a relative rolling movement between said hob and blank in themanner of a gear meshing with its mate gear.

18. The method of cutting a 'pair of gears comprising cutting one memberof the pair wth a taper hob of constant pitch by rotating said hob inintermeshing engagement with a continuously rotating gear blank whileimparting a relative feed movement between said hob and blank so that infinish cuttin position the hob sweeps out the whole finishe toothsurface of the blank, and in cutting the other member of the pair byrotating a taper hob of constant pitch in intermeshing cuttingengagement with a continuously rotating gear blank while imparting arelative rolling movement between said hob and blank in the manner of agear meshing with its mate gear.

19. The method of'cutting a pair of gears noeaeee having longitudinallycurved teeth comprising cutting one member by rotating atool, having itscutting portions arranged in a continuous thread, in continuousinter-meshing engagement with a rotating gear blank while impartingarelative feed movement between said tool and blank parallel with theblank axis so that the tool in finish cutting position sweeps out thewhole finished tooth surface of the blank, and in cutting the othermember by rotating a tool of the same structureas the first tool incontinuous intermeshing engageploying a taper hob, of a constructionother.

than that of the gear with which the gear being cut is to mesh, androtating said hob in intermeshing engagement with a *continu-.

ously rotating gear blank while impartinga relative feed movementbetween said hob and blank so that in finish cutting position the hobwill sweep out the whole finished tooth surface of the blank.

21. The method of cutting a pair of gears having longitudinally curvedteeth comprising cutting one member by rotating a tool, having itscutting portions arranged in a continuous thread, in continuousintermeshing engagement with a rotating gear blank while imparting arelative feed movement between said tool and blank so that in finishcutting position the tool sweeps out the whole finished tooth surface ofthe blank, and in cutting the other member by rotating a tool, havingits cutting portions arranged in a continuous thread, in continuousintermeshing engagement with a rotating gear blank while imparting arelative rolling movement between said last named tool and blank in theI manner of a gear meshing with its mate gear.

22. The method of cutting a gear provided with longitudinally curvedteeth on its side face which tfonsists in rotating a hob ofconstantpitch in a plane "ofiset from its axis in continuous cutting andindexing engagement with a gear blank while maintalning the axis of thehob in fixed offset and angular relation to the axis ofthe blank so thatin finish cutting position the hob sweeps out the whole finished toothsurface of the blank. i

23. The method of c ttingya gear provided with longitudinally curvedteeth on its side face which consists in rotat ng a hob of constantpitch in engagement with a continuously rotating gear blank whileimparting a relative rolling motion between the hob and blank in themanner of a gear meshing with its mate gear.

24. The method of cutting a gear provided with longitudinally curvedteeth on its side iso aoeaese stant pitch in a plane offset from itsaxis in engagement with a continuously rotating gear blank whileimparting a relative rolling motion between the hob and blank in themanner of a gear meshing with its mate gear.

25. The method of cutting a longitudinally curved tooth tapered gearwhich consists in rotating a taper hob 1n engagement with a continuouslyrotating gear blank while imparting a relative rolling motion betweenthe hob and blank in the manner of a gear meshing with its mate gear.

26. The method of cutting a longitudinally curved tooth tapered gearwhich consists in I rotating a taper h'ob of constant pitch inengagement with a continuously rotating gear blank while imparting arelative rolling motion between the hob and blank in the manner of agear meshing with its mate gear.

2?. The method of cutting'a longitudinally curved tooth tapered gearwhich consists in rotating a taper hob of constant pitch in a planeoffset from its axis in engagement with a continuously rotating gearblank while imparting a relative rolling motion between the hob andblank in the manner of a gear meshing with its mate gear.

28. The method of cutting a pair of gears which consists in cutting onemember of the pair by rotating a hob in engagement with a continuouslyrotating gear blank while maintaining the angular relation between thehob and blank axes fixed, so that in finish cutting position the hobsweeps out the Whole finished tooth surface of the blank, and in cuttingthe other member of the pair by rotating a hob in engagement with acontinuously rotating gear blank while imparting a relative rollingmotion between the hob and blank.

29. The method of cutting a pair of gears which consists in cutting onemember of the pair by rotating the hob in engagement with 4 acontinuously rotating gear blank While maintaining a fixed angularrelation between the hob and blank axes, so that in finish cuttingposition the hob sweeps out the whole finished tooth surface of theblank, and in cutting the other member of the pair by rotating a hob inengagement with a continuously rotating gear blank while imparting arelative rolling motion between the hob and blank as of a gear rollingon the first gear.

ERNEST WILDHABER.

